名校
1 . 已知数列
满足:
(其中
且
),
为数列
的前
项和.
(1)若
,求
的值;
(2)求数列
的通项公式
;
(3)当
时,数列
中是否存在三项构成等差数列,若存在,请求出此三项;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84e4a6ba8df6cbe80b09da11a40df0bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78fbecca12ee62538020483fd55a2109.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9805d9c45198c7a249f317222f564999.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2251391555522aa9598f3c6587c011f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1c3ea872a20fdc1843cb5ffce8a554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
名校
2 . 给定数列
,若数列
中任意(不同)两项之和仍是该数列中的一项,则称该数列是“封闭数列”.
(1)已知数列
的通项公式为
,试判断
是否为封闭数列,并说明理由;
(2)已知数列
满足
且
,设
是该数列
的前
项和,试问:是否存在这样的“封闭数列”
,使得对任意
都有
,且
,若存在,求数列
的首项
的所有取值;若不存在,说明理由;
(3)证明等差数列
成为“封闭数列”的充要条件是:存在整数
,使
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac7f82f00fe6163833431241820687ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d716ccbf4313122355c270fe2e67b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bf4000fec5bf94d56935108d72af3c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1d236a265a6cc0f3d06a0e568ffa907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9bf52f91d72053371b83ea0d713047a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
(3)证明等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87a9ef1f87936695fb681df932efd10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c54680219b440350ffc5f1f43b3b78e0.png)
您最近一年使用:0次
2020-01-01更新
|
583次组卷
|
3卷引用:2018年上海市青浦区高三4月质量调研(二模)数学试题
名校
3 . 对于任意
,若数列
满足
,则称这个数列为“K数列”.
(1)已知数列:1,
,
是“K数列”,求实数m的取值范围;
(2)是否存在首项为-1的无穷等差数列
为“K数列”,且其前n项和
满足:
,若存在,求出
的通项公式;若不存在,请说明理由;
(3)已知各项均为正整数的等比数列
(至少有4项)为“K数列”,数列
不是“K数列”,若
,是否存在
,使
为“K数列”?若存在,请求出,
若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdb5679fa7c34fc2235d2a54d189cfbb.png)
(1)已知数列:1,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0623207595425920f16e76a7f8f268b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8d7b4bb12628d5ed455d814b8aafa1f.png)
(2)是否存在首项为-1的无穷等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f5011f62c285c73e9baddd16f485777.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f11ccfdc706f6b34fca9fe0b6861f98f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f5011f62c285c73e9baddd16f485777.png)
(3)已知各项均为正整数的等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f5011f62c285c73e9baddd16f485777.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bed6e14fb838e9ebfcfc65c8c45c5268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dec647aa5a790540546327105909ff3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f5011f62c285c73e9baddd16f485777.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f5011f62c285c73e9baddd16f485777.png)
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名校
4 . 设
,若存在
,使得
,且对任意
,均有
(即
是一个公差为
的等差数列),则称数列
是一个长度为
的“弱等差数列”.
(1)判断下列数列是否为“弱等差数列”,并说明理由.
①1,3,5,7,9,11;
②2,
,
,
,
.
(2)证明:若
,则数列
为“弱等差数列”.
(3)对任意给定的正整数
,若
,是否总存在正整数
,使得等比数列:
是一个长度为
的“弱等差数列”?若存在,给出证明;若不存在,请说明理由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05ed0ba6536a760f14dd88b4ecd1f05a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4739759b4a0c11f454486a6c3eb57ac2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe9dc7f4f19648bdf46002b0347bbd26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41a700b0d0945efecde4f1640c3e7269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15856931c7f3a441f7487ee8250cff67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f9b7c68f6cb3dfe73974a9d256854b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20655342f9ace8b50a50f5eae6f37beb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)判断下列数列是否为“弱等差数列”,并说明理由.
①1,3,5,7,9,11;
②2,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ad4668cc927e277289b2af718f0d91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6648bc986a558fa32e752d28d3a68431.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa6ec171ea9f8e9be9bf13baea05cd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/955079ed2708734e50394387cf40c111.png)
(2)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29719d33af813b84dae0191ae5c92a00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c14d9ae06f864498048d55088ff4e6.png)
(3)对任意给定的正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/003298774340282d4710ce2a1cb6f7b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1adc8b199fd10b888a832adaa1a80f3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d222ee9268e028c1a59dc2ec35d7875f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2018·上海浦东新·三模
名校
5 . 设
,若无穷数列
满足:对所有整数
,都成立
,则称
“
-折叠数列”.
(1)求所有的实数
,使得通项公式为
的数列
是
-折叠数列;
(2)给定常数
,是否存在数列
,使得对所有
,
都是
-折叠数列,且
的各项中恰有
个不同的值?证明你的结论;
(3)设递增数列
满足
.已知如果对所有
,
都是
-折叠数列,则
的各项中至多只有
个不同的值,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a949b947e9961d4d68bfeb4e24ef40f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98251cd3c3e36825493a3f83b0ac9d6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9cdd87bcc6088bea7dc1f24387b0502.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)求所有的实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6290fabfee064ca7296364c2011c16ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
(2)给定常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/270672a95f2a5349bc440c53b5dd4a12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a949b947e9961d4d68bfeb4e24ef40f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dbc76e88046029a006e48b6b58823d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fbf39f278f6fcfbd30de4a1ad65e5bf.png)
(3)设递增数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4818b2c2d51316638cf39039d6cb4d11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f74927b7593fd0b4f218b3806e3025dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a949b947e9961d4d68bfeb4e24ef40f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681ae1522a36768618f7ddaf74abbb7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b037996f28c91402cff9c883c99a8e6.png)
您最近一年使用:0次
6 . 对于
个实数构成的集合
,记
.
已知由
个正整数构成的集合
(
)满足:对于任意不大于
的正整数
,均存在集合
的一个子集,使得该子集的所有元素之和等于
.
(1)试求
,
的值;
(2)求证:“
成等差数列”的充要条件是“
”;
(3)若
,求证:
的最小值为
;并求
取最小值时,
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4c4d0c7c0168f789264c0331e6e4a66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c5b9611e7c8658f96c9323ada6b69bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/652b1ba1a05e8cfc29cfb4b2c009d1d1.png)
已知由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e895d0fd41b86910f8b3948c23108c0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/282f374bf5ef53effa71c745f8d4cde0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/340670e6a6a7d9ef889c3c4c56ce6837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)试求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b42791b77924729f7e31712177b26af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb5ca241bb7c313ef0366d3ddba93bc.png)
(2)求证:“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b63e64d9d9cf9b4fa07a1b685d41bce6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/055a0a67f653ff49f037255d74c26c82.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22bd7ad67c3cfa996577f4b9985d8782.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c79c562343bd2362a979662d3865020c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bfccafa83afe5ee21eab6ef2b2c8852.png)
您最近一年使用:0次
名校
7 . 已知
,
都是各项为正数的数列,且
,
.对任意的正整数n,都有
,
,
成等差数列,
,
,
成等比数列.
(1)求数列
和
的通项公式;
(2)若存在p>0,使得集合M=
恰有一个元素,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30052c54892789bc548374412730ede4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be85b6de3f99238545d0c51b4c79433e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090426eb29836bc30c006b3739c08057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49b4835c4cd402232ba87fd8a9295d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e95931effbd59c43e8ed1ea09962b84f.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若存在p>0,使得集合M=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42ff54cc58af803b3ec302829a4eef59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2018-12-12更新
|
843次组卷
|
2卷引用:【全国百强校】江苏省南师大附中2019届高三年级第一学期期中考试数学试题
8 . 已知数列
满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/674f0a8b77879e3644e6f40b139e0d27.png)
为正常数.
(1)求证:对于一切
恒成立;
(2)若数列
为等差数列,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/674f0a8b77879e3644e6f40b139e0d27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
(1)求证:对于一切
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf444c2cbfc0df2cc23fbab8d7654b8.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
您最近一年使用:0次
9 . 设
是首项为
,公差为d的等差数列,
是首项为
,公比为q的等比数列.
(1)设
,若
对
均成立,求d的取值范围;
(2)若
,证明:存在
,使得
对
均成立,并求
的取值范围(用
表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74aef4b54e5d8f632c926960b2e4c7b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3e68bee3f515ef798679ac95b1eb9bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4967a0f83ec59ad5a74ce1c3653a2451.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7791ac8b85b10c06d7f14eb122565e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7b33ff8346b233bd4721e7c1b67488e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3e68bee3f515ef798679ac95b1eb9bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ec3452165ffeaf9e66306b9737eea4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e58095b1abf1531476571d1cb21330.png)
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2018-06-10更新
|
5755次组卷
|
19卷引用:2018年全国普通高等学校招生统一考试数学(江苏卷)
2018年全国普通高等学校招生统一考试数学(江苏卷)(已下线)2018年高考题及模拟题汇编 【理科】4.数列与不等式(已下线)2018年高考题及模拟题汇编 【文科】4.数列与不等式(已下线)专题14 数列的综合应用-《巅峰冲刺2020年高考之二轮专项提升》(江苏)专题18 常用逻辑用语-《巅峰冲刺2020年高考之二轮专项提升》[江苏]江苏省南京市第二十九中学2018-2019学年高三下学期4月月考数学试题(已下线)专题12 数列——三年(2018-2020)高考真题理科数学分项汇编(已下线)专题14 数列综合-五年(2016-2020)高考数学(文)真题分项(已下线)专题14 数列综合-五年(2016-2020)高考数学(理)真题分项(已下线)专题20 数列的综合-2020年高考数学母题题源解密(江苏专版)(已下线)专题19 数列的求和问题-十年(2011-2020)高考真题数学分项(已下线)考点02 全称量词与存在量词、充要条件-2021年高考数学三年真题与两年模拟考点分类解读(新高考地区专用)(已下线)预测07 数列-【临门一脚】2020年高考数学三轮冲刺过关(江苏专用)(已下线)预测08 不等式、推理与证明-【临门一脚】2020年高考数学三轮冲刺过关(江苏专用)(已下线)专题6.5 数列的综合应用(练)【理】-《2020年高考一轮复习讲练测》(已下线)考点21 数列的概念与简单表示法-备战2022年高考数学(理)一轮复习考点帮(已下线)专题2 数列的最大项与最小项 微点3 判断数列的最大(小)项之导数法(已下线)专题21 数列解答题(理科)-3(已下线)专题21 数列解答题(文科)-2
10 . 已知数列
中
,前
项和为
,若对任意的
,均有
(
是常数,且
)成立,则称数列
为“
数列”.
(1)若数列
为“
数列”,求数列
的前
项和
;
(2)若数列
为“
数列”,且
为整数,试问:是否存在数列
,使得
对一切
,
恒成立?如果存在,求出这样数列
的
的所有可能值,如果不存在,请说明理由;
(3)若数列
为“
数列”,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2002a484aeb332ebd6d4d78d4abe5b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e36bff57bcfa86432b340e25e51d42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/808e14bce93904b666fa39935c027cc9.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62b96ee0875a6bcaf9371fb9cfd7eae4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/798548b5fbb631a0828621581a741f06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc0271e3c9413df9fc330085ad92607f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/808e14bce93904b666fa39935c027cc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/849d7e67c117f598d732bf86615e1f57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91b5f3cd0c7207a6517c6822e08ae78.png)
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